I've downloaded the package but as I'm trying to open it I get this message:

Archive: /home/agnes/Downloads/ggtranslate.exe
[/home/agnes/Downloads/ggtranslate.exe]
End-of-central-directory signature not found. Either this file is not
a zipfile, or it constitutes one disk of a multi-part archive. In the
latter case the central directory and zipfile comment will be found on
the last disk(s) of this archive.
zipinfo: cannot find zipfile directory in one of /home/agnes/Downloads/ggtranslate.exe or
/home/agnes/Downloads/ggtranslate.exe.zip, and cannot find /home/agnes/Downloads/ggtranslate.exe.ZIP, period.

Google Desktop Translator is a Java application that runs on Ubuntu if Java was installed. The file you downloaded obviously is designed to install and uncompress from Windows or (see Javier Rivera's comment) may be another third party Windows program. Both will not work in Ubuntu.

Download the appropriate .zip file directly from Google with this link:

Uncompress the files, open a terminal, cd to your installation directory and run

java -jar google-translate-desktop-0.52.jar

The program window should now open:

Unfortunately in version 0.52 this window has no decoration and cannot be moved, but there is full translation functionality. For quitting or for program settings a status icon is generated in the GNOME panel. Windows decoration is present in the beta version only that has a slightly reduced functionality.

Just ran run-linux.sh and java -jar google-translate-desktop-0.52.jar and got this msg: Could not open the file /home/agnes/Downloads/go…ranslate-desktop-0.52.jar. gedit has not been able to detect the character coding. Please check that you are not trying to open a binary file. Select a character coding from the menu and try again.
– AgneseJan 20 '11 at 12:16

I was just able to test this on my 10.04 am64 (see screenshots) with no further steps. Java does not find the jar file on your system. Make sure there are no typing errors and the .jar file is really present in the directory from where you run java (e.g. ls lists google-translate-desktop-0.52.jar before you invoke the java command)
– TakkatJan 20 '11 at 17:28

Setting up and configuring the 'translate highlighted text' script

To be able to use the script, firstly install libnotify-bin (so the script can send desktop notifications), wget (to retrieve the translation from Google) and xsel (which is used to get the currently highlighted text). In Ubuntu, Linux Mint, etc. install them using the following command:

and paste it in a new file - let's call it notitrans (well, you can call it whatever you want, but that's how I'll refer to it from now on).

In the script above, replace tl=en with the language into which you want the text to be translated, for instance tl=ru for Russian, tl=fr for French and so on.

After you're done, save the file in your home directory and make it executable using the following command:

chmod +x ~/notitrans

Place the script in your $PATH - for instance, to copy the script to /usr/local/bin/, use the following command:

sudo mv ~/notitrans /usr/local/bin/

To be able to use the script, you can assign it a custom keyboard shortcut. Doing this depends on your desktop environment.

On GNOME (and Unity), you can do this by going to System Settings > Keyboard > Shortcuts > Custom Shortcuts, where you'll need to click "+" to add a new keyboard shortcut. Here, enter any name you want for the new custom shortcut and "notitrans" as the command:

And finally, assign a keyboard shortcut to the newly added command by clicking on it and then holding down the keys you want to assign to it. Make sure the keyboard shortcut is not already in use!

Optional: variations of the 'translate highlighted text' script

Display the translation with Zenity (which allows the text to be copied) instead of using desktop notifications: